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				<span style="position: absolute;left:15px;bottom:15px;width:90%;"><font class="view-text" style="color:#fcfcfc;font-size:25px">题解 CF848E 【Days of Floral Colours】</font><br><a href="/tags/2021/" class="tag"><span  style="background-color: rgb(52, 152, 219);">2021</span></a>&nbsp;<a href="/tags/生成函数/" class="tag"><span  style="background-color: rgb(231, 76, 60);">生成函数</span></a>&nbsp;<a href="/tags/题解/" class="tag"><span  style="background-color: rgb(82, 196, 26);">题解</span></a></span>
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                <h2 id="_1">题意</h2>
<p>咕咕咕</p>
<h2 id="_2">题解</h2>
<p>太菜了，就来复读一下吧，题解是不会交了。</p>
<p>
<script type="math/tex">\rm \color{black}Z\color{red}LC\_AK</script>嫌我太菜了不肯教我/kk</p>
<p>降维打击赛高！！</p>
<p>一对相对的相同颜色的花把环分成两段，两段是相同的。那么考虑把半边环分成了 <script type="math/tex">k</script> 段，显然会算重 <script type="math/tex">k</script> 次，除 <script type="math/tex">k</script> 即可。</p>
<p>那么考虑一段不含有相对的相同颜色的段，可以一次两个 <script type="math/tex">(i,i+1)</script>，也可以一次四个 <script type="math/tex">(i,i+2),(i+1,i+3)</script>，因此长度为 <script type="math/tex">n</script> 的段的方案 <script type="math/tex">g_n=g_{n-2}+g_{n-4}</script>，<script type="math/tex">g_2=g_4=1</script>。</p>
<p>不难写出封闭形式 <script type="math/tex">F(x)=\dfrac1{1-x^2-x^4}</script>
</p>
<p>那么每一段只有三种可能：首位都不跨越，一端跨越，两段跨越</p>
<p>考虑首尾都不跨越的贡献，对于 <script type="math/tex">x^n</script> 贡献为 <script type="math/tex">n^2</script>。</p>
<p>
<script type="math/tex">xF'(x)</script> 相当于把 <script type="math/tex">F(x)</script> 的 <script type="math/tex">x^n</script> 乘了 <script type="math/tex">n</script>，因此 <script type="math/tex">F_0(x)=x\times x\times (x\times F'(x))'</script>。多出来的 <script type="math/tex">x</script> 是因为第一个相对的也算在这一段内。</p>
<p>那么有一边跨越实际上是 <script type="math/tex">x^n</script> 系数乘上 <script type="math/tex">(n+1)^2</script>，<script type="math/tex">(x\times F(x))'</script> 就实现把 <script type="math/tex">x^n</script> 系数乘 <script type="math/tex">n+1</script> ，因此 <script type="math/tex">F_1(x)=x^2\times (x\times (x\times F(x))')'</script>
</p>
<p>那么同理有两边跨越的就是 <script type="math/tex">F_2(x)=x^2\times (x\times (x^2\times F(x))')'</script>
</p>
<p>那么考虑两段接在一起，第一段为 <script type="math/tex">A_0,A_1,A_2</script>，第二段为 <script type="math/tex">B_0,B_1,B_2</script>。（分别为两段都不跨越、一端跨越、两端跨越），得到新的生成函数：
<script type="math/tex; mode=display">
\begin{aligned}
C_0(x)=A_0(x)B_0(x)+A_1(x)B_1(x)\\
C_1(x)=A_0(x)B_2(x)+A_1(x)B_2(x)\\
C_2(x)=A_1(x)B_1(x)+A_2(x)B_2(x)\\
\end{aligned}
</script>
因此想到矩阵形式：
<script type="math/tex; mode=display">M(x)=\left[\begin{matrix}F_0(x)&F_1(x)\\F_1(x)&F_2(x)\end{matrix}\right]</script>
最终的答案即为 
<script type="math/tex; mode=display">A(x)=\sum_{k=1}\frac{M^k(x)}{k}</script>
主对角线和 <script type="math/tex">x^n</script> 的系数乘 <script type="math/tex">n</script>，因为我们并没有考虑开始位置。
<script type="math/tex; mode=display">
\begin{aligned}
B(x)&=x\times A'(x)=x\sum_{k=1}M^{k-1}(x)M'(x)\\
&=\frac{xM'(x)}{1-M(x)}
\end{aligned}
</script>
的主对角线和的系数。</p>
<p>主对角线的和是这么个玩意儿：
<script type="math/tex; mode=display">\frac{24 x^3 + 4 x^4 + 144 x^5 - 4 x^6 + 348 x^7 - 128 x^8 + 240 x^9 + 28 x^{10} + 188 x^{11} - 68 x^{12} + 16 x^{13} + 4 x^{15}}{1 - 4 x^2 - 8 x^3 + x^4 - 16 x^5 + 10 x^6 - 4 x^7 + 12 x^8 + 48 x^9 - 26 x^{10} + 44 x^{11} - 15 x^{12} + 16 x^{13} + 4 x^{14} + 4 x^{15} + x^{16}}
</script>
通项长这样：</p>
<p><img alt="" src="/img/1kp13qdf.png"></p>
<p>好吧通项没有前途还是老老实实写线性递推吧。</p>
<p>考虑 
<script type="math/tex; mode=display">
\begin{aligned}
P(x)&=24 x^3 + 4 x^4 + 144 x^5 - 4 x^6 + 348 x^7 - 128 x^8 + 240 x^9 +  28 x^{10} + 188 x^{11} - 68 x^{12} + 16 x^{13} + 4 x^{15}\\
Q(x)&=1 - 4 x^2 - 8 x^3 + x^4 - 16 x^5 + 10 x^6 - 4 x^7 + 12 x^8 + 48 x^9 - 26 x^{10} + 44 x^{11} - 15 x^{12} + 16 x^{13} + 4 x^{14} + 4 x^{15} + x^{16}\\
C(x)&=1-Q(x)\\
G(x)&=\frac{P(x)}{1-C(x)}\Longrightarrow G(x)=C(x)G(x)+P(x)
 \end{aligned}
 </script>
 可以线性递推了的说。</p>
<p>矩阵直接上是 <script type="math/tex">O(16^3\log n)</script> 的，不过众所周知矩阵乘法可以写成多项式取模来做到 <script type="math/tex">O(16^2\log n)</script>。这里直接写暴力的多项式取模即可。</p>
<h2 id="_3">代码</h2>
<div class="highlight"><pre><span></span><code><span class="linenos" data-linenos=" 1 "></span><span class="cp">#include</span><span class="cpf">&lt;bits/stdc++.h&gt;</span><span class="cp"></span>
<span class="linenos" data-linenos=" 2 "></span><span class="k">namespace</span> <span class="n">in</span><span class="p">{</span>
<span class="linenos" data-linenos=" 3 "></span>    <span class="cp">#ifndef slow</span>
<span class="linenos" data-linenos=" 4 "></span>    <span class="kt">char</span> <span class="n">buf</span><span class="p">[</span><span class="mi">1</span><span class="o">&lt;&lt;</span><span class="mi">21</span><span class="p">],</span><span class="o">*</span><span class="n">p1</span><span class="o">=</span><span class="n">buf</span><span class="p">,</span><span class="o">*</span><span class="n">p2</span><span class="o">=</span><span class="n">buf</span><span class="p">;</span>
<span class="linenos" data-linenos=" 5 "></span>    <span class="kr">inline</span> <span class="kt">int</span> <span class="n">getc</span><span class="p">(){</span><span class="k">return</span> <span class="n">p1</span><span class="o">==</span><span class="n">p2</span><span class="o">&amp;&amp;</span><span class="p">(</span><span class="n">p2</span><span class="o">=</span><span class="p">(</span><span class="n">p1</span><span class="o">=</span><span class="n">buf</span><span class="p">)</span><span class="o">+</span><span class="n">fread</span><span class="p">(</span><span class="n">buf</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="o">&lt;&lt;</span><span class="mi">21</span><span class="p">,</span><span class="n">stdin</span><span class="p">),</span><span class="n">p1</span><span class="o">==</span><span class="n">p2</span><span class="p">)</span><span class="o">?</span><span class="nl">EOF</span><span class="p">:</span><span class="o">*</span><span class="n">p1</span><span class="o">++</span><span class="p">;}</span>
<span class="linenos" data-linenos=" 6 "></span>    <span class="cp">#else</span>
<span class="linenos" data-linenos=" 7 "></span>    <span class="kr">inline</span> <span class="kt">int</span> <span class="n">getc</span><span class="p">(){</span><span class="k">return</span> <span class="nf">getchar</span><span class="p">();}</span>
<span class="linenos" data-linenos=" 8 "></span>    <span class="cp">#endif</span>
<span class="linenos" data-linenos=" 9 "></span>    <span class="k">template</span> <span class="o">&lt;</span><span class="k">typename</span> <span class="nc">T</span><span class="o">&gt;</span><span class="kr">inline</span> <span class="kt">void</span> <span class="n">read</span><span class="p">(</span><span class="n">T</span><span class="o">&amp;</span> <span class="n">t</span><span class="p">){</span>
<span class="linenos" data-linenos="10 "></span>        <span class="n">t</span><span class="o">=</span><span class="mi">0</span><span class="p">;</span><span class="kt">int</span> <span class="n">f</span><span class="o">=</span><span class="mi">0</span><span class="p">;</span><span class="kt">char</span> <span class="n">ch</span><span class="o">=</span><span class="n">getc</span><span class="p">();</span><span class="k">while</span> <span class="p">(</span><span class="o">!</span><span class="n">isdigit</span><span class="p">(</span><span class="n">ch</span><span class="p">)){</span><span class="k">if</span><span class="p">(</span><span class="n">ch</span><span class="o">==</span><span class="sc">&#39;-&#39;</span><span class="p">)</span><span class="n">f</span> <span class="o">=</span> <span class="mi">1</span><span class="p">;</span><span class="n">ch</span><span class="o">=</span><span class="n">getc</span><span class="p">();}</span>
<span class="linenos" data-linenos="11 "></span>        <span class="k">while</span><span class="p">(</span><span class="n">isdigit</span><span class="p">(</span><span class="n">ch</span><span class="p">)){</span><span class="n">t</span><span class="o">=</span><span class="n">t</span><span class="o">*</span><span class="mi">10</span><span class="o">+</span><span class="n">ch</span><span class="mi">-48</span><span class="p">;</span><span class="n">ch</span> <span class="o">=</span> <span class="n">getc</span><span class="p">();}</span><span class="k">if</span><span class="p">(</span><span class="n">f</span><span class="p">)</span><span class="n">t</span><span class="o">=-</span><span class="n">t</span><span class="p">;</span>
<span class="linenos" data-linenos="12 "></span>    <span class="p">}</span>
<span class="linenos" data-linenos="13 "></span>    <span class="k">template</span> <span class="o">&lt;</span><span class="k">typename</span> <span class="nc">T</span><span class="p">,</span><span class="k">typename</span><span class="p">...</span> <span class="n">Args</span><span class="o">&gt;</span> <span class="kr">inline</span> <span class="kt">void</span> <span class="n">read</span><span class="p">(</span><span class="n">T</span><span class="o">&amp;</span> <span class="n">t</span><span class="p">,</span> <span class="n">Args</span><span class="o">&amp;</span><span class="p">...</span> <span class="n">args</span><span class="p">){</span><span class="n">read</span><span class="p">(</span><span class="n">t</span><span class="p">);</span><span class="n">read</span><span class="p">(</span><span class="n">args</span><span class="p">...);}</span>
<span class="linenos" data-linenos="14 "></span><span class="p">}</span>
<span class="linenos" data-linenos="15 "></span><span class="k">namespace</span> <span class="n">out</span><span class="p">{</span>
<span class="linenos" data-linenos="16 "></span>    <span class="kt">char</span> <span class="n">buffer</span><span class="p">[</span><span class="mi">1</span><span class="o">&lt;&lt;</span><span class="mi">21</span><span class="p">];</span><span class="kt">int</span> <span class="n">p1</span><span class="o">=</span><span class="mi">-1</span><span class="p">;</span><span class="k">const</span> <span class="kt">int</span> <span class="n">p2</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span><span class="o">&lt;&lt;</span><span class="mi">21</span><span class="p">)</span><span class="mi">-1</span><span class="p">;</span>
<span class="linenos" data-linenos="17 "></span>    <span class="kr">inline</span> <span class="kt">void</span> <span class="n">flush</span><span class="p">(){</span><span class="n">fwrite</span><span class="p">(</span><span class="n">buffer</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="n">p1</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span><span class="n">stdout</span><span class="p">),</span><span class="n">p1</span><span class="o">=</span><span class="mi">-1</span><span class="p">;}</span>
<span class="linenos" data-linenos="18 "></span>    <span class="kr">inline</span> <span class="kt">void</span> <span class="n">putc</span><span class="p">(</span><span class="k">const</span> <span class="kt">char</span> <span class="o">&amp;</span><span class="n">x</span><span class="p">)</span> <span class="p">{</span><span class="k">if</span><span class="p">(</span><span class="n">p1</span><span class="o">==</span><span class="n">p2</span><span class="p">)</span><span class="n">flush</span><span class="p">();</span><span class="n">buffer</span><span class="p">[</span><span class="o">++</span><span class="n">p1</span><span class="p">]</span><span class="o">=</span><span class="n">x</span><span class="p">;}</span>
<span class="linenos" data-linenos="19 "></span>    <span class="k">template</span> <span class="o">&lt;</span><span class="k">typename</span> <span class="nc">T</span><span class="o">&gt;</span><span class="kt">void</span> <span class="n">write</span><span class="p">(</span><span class="n">T</span> <span class="n">x</span><span class="p">)</span> <span class="p">{</span>
<span class="linenos" data-linenos="20 "></span>        <span class="k">static</span> <span class="kt">char</span> <span class="n">buf</span><span class="p">[</span><span class="mi">15</span><span class="p">];</span><span class="k">static</span> <span class="kt">int</span> <span class="n">len</span><span class="o">=</span><span class="mi">-1</span><span class="p">;</span><span class="k">if</span><span class="p">(</span><span class="n">x</span><span class="o">&gt;=</span><span class="mi">0</span><span class="p">){</span><span class="k">do</span><span class="p">{</span><span class="n">buf</span><span class="p">[</span><span class="o">++</span><span class="n">len</span><span class="p">]</span><span class="o">=</span><span class="n">x</span><span class="o">%</span><span class="mi">10</span><span class="o">+</span><span class="mi">48</span><span class="p">,</span><span class="n">x</span><span class="o">/=</span><span class="mi">10</span><span class="p">;}</span><span class="k">while</span> <span class="p">(</span><span class="n">x</span><span class="p">);}</span><span class="k">else</span><span class="p">{</span><span class="n">putc</span><span class="p">(</span><span class="sc">&#39;-&#39;</span><span class="p">);</span><span class="k">do</span> <span class="p">{</span><span class="n">buf</span><span class="p">[</span><span class="o">++</span><span class="n">len</span><span class="p">]</span><span class="o">=-</span><span class="p">(</span><span class="n">x</span><span class="o">%</span><span class="mi">10</span><span class="p">)</span><span class="o">+</span><span class="mi">48</span><span class="p">,</span><span class="n">x</span><span class="o">/=</span><span class="mi">10</span><span class="p">;}</span><span class="k">while</span><span class="p">(</span><span class="n">x</span><span class="p">);}</span>
<span class="linenos" data-linenos="21 "></span>        <span class="k">while</span> <span class="p">(</span><span class="n">len</span><span class="o">&gt;=</span><span class="mi">0</span><span class="p">)</span><span class="n">putc</span><span class="p">(</span><span class="n">buf</span><span class="p">[</span><span class="n">len</span><span class="p">]),</span><span class="o">--</span><span class="n">len</span><span class="p">;</span>
<span class="linenos" data-linenos="22 "></span>    <span class="p">}</span>
<span class="linenos" data-linenos="23 "></span><span class="p">}</span>
<span class="linenos" data-linenos="24 "></span><span class="k">using</span> <span class="k">namespace</span> <span class="n">std</span><span class="p">;</span>
<span class="linenos" data-linenos="25 "></span><span class="k">const</span> <span class="kt">int</span> <span class="n">mod</span><span class="o">=</span><span class="mi">998244353</span><span class="p">;</span>
<span class="linenos" data-linenos="26 "></span><span class="k">template</span><span class="o">&lt;</span><span class="k">const</span> <span class="kt">int</span> <span class="n">mod</span><span class="o">&gt;</span>
<span class="linenos" data-linenos="27 "></span><span class="k">struct</span> <span class="nc">modint</span><span class="p">{</span>
<span class="linenos" data-linenos="28 "></span>    <span class="kt">int</span> <span class="n">x</span><span class="p">;</span>
<span class="linenos" data-linenos="29 "></span>    <span class="n">modint</span><span class="o">&lt;</span><span class="n">mod</span><span class="o">&gt;</span><span class="p">(</span><span class="kt">int</span> <span class="n">o</span><span class="o">=</span><span class="mi">0</span><span class="p">){</span><span class="n">x</span><span class="o">=</span><span class="n">o</span><span class="o">%</span><span class="n">mod</span><span class="p">;(</span><span class="n">x</span><span class="o">&lt;</span><span class="mi">0</span><span class="p">)</span><span class="o">&amp;&amp;</span><span class="p">(</span><span class="n">x</span><span class="o">+=</span><span class="n">mod</span><span class="p">);}</span>
<span class="linenos" data-linenos="30 "></span>    <span class="n">modint</span><span class="o">&lt;</span><span class="n">mod</span><span class="o">&gt;</span> <span class="o">&amp;</span><span class="k">operator</span> <span class="o">=</span> <span class="p">(</span><span class="kt">int</span> <span class="n">o</span><span class="p">){</span><span class="k">return</span> <span class="n">x</span><span class="o">=</span><span class="n">o</span><span class="p">,</span><span class="o">*</span><span class="k">this</span><span class="p">;}</span>
<span class="linenos" data-linenos="31 "></span>    <span class="n">modint</span><span class="o">&lt;</span><span class="n">mod</span><span class="o">&gt;</span> <span class="o">&amp;</span><span class="k">operator</span> <span class="o">+=</span><span class="p">(</span><span class="n">modint</span><span class="o">&lt;</span><span class="n">mod</span><span class="o">&gt;</span> <span class="n">o</span><span class="p">){</span><span class="k">return</span> <span class="n">x</span><span class="o">=</span><span class="n">x</span><span class="o">+</span><span class="n">o</span><span class="p">.</span><span class="n">x</span><span class="o">&gt;=</span><span class="n">mod</span><span class="o">?</span><span class="n">x</span><span class="o">+</span><span class="n">o</span><span class="p">.</span><span class="n">x</span><span class="o">-</span><span class="nl">mod</span><span class="p">:</span><span class="n">x</span><span class="o">+</span><span class="n">o</span><span class="p">.</span><span class="n">x</span><span class="p">,</span><span class="o">*</span><span class="k">this</span><span class="p">;}</span>
<span class="linenos" data-linenos="32 "></span>    <span class="n">modint</span><span class="o">&lt;</span><span class="n">mod</span><span class="o">&gt;</span> <span class="o">&amp;</span><span class="k">operator</span> <span class="o">-=</span><span class="p">(</span><span class="n">modint</span><span class="o">&lt;</span><span class="n">mod</span><span class="o">&gt;</span> <span class="n">o</span><span class="p">){</span><span class="k">return</span> <span class="n">x</span><span class="o">=</span><span class="n">x</span><span class="o">-</span><span class="n">o</span><span class="p">.</span><span class="n">x</span><span class="o">&lt;</span><span class="mi">0</span><span class="o">?</span><span class="n">x</span><span class="o">-</span><span class="n">o</span><span class="p">.</span><span class="n">x</span><span class="o">+</span><span class="nl">mod</span><span class="p">:</span><span class="n">x</span><span class="o">-</span><span class="n">o</span><span class="p">.</span><span class="n">x</span><span class="p">,</span><span class="o">*</span><span class="k">this</span><span class="p">;}</span>
<span class="linenos" data-linenos="33 "></span>    <span class="n">modint</span><span class="o">&lt;</span><span class="n">mod</span><span class="o">&gt;</span> <span class="o">&amp;</span><span class="k">operator</span> <span class="o">*=</span><span class="p">(</span><span class="n">modint</span><span class="o">&lt;</span><span class="n">mod</span><span class="o">&gt;</span> <span class="n">o</span><span class="p">){</span><span class="k">return</span> <span class="n">x</span><span class="o">=</span><span class="mf">1l</span><span class="n">l</span><span class="o">*</span><span class="n">x</span><span class="o">*</span><span class="n">o</span><span class="p">.</span><span class="n">x</span><span class="o">%</span><span class="n">mod</span><span class="p">,</span><span class="o">*</span><span class="k">this</span><span class="p">;}</span>
<span class="linenos" data-linenos="34 "></span>    <span class="n">modint</span><span class="o">&lt;</span><span class="n">mod</span><span class="o">&gt;</span> <span class="o">&amp;</span><span class="k">operator</span> <span class="o">^=</span><span class="p">(</span><span class="kt">int</span> <span class="n">b</span><span class="p">){</span>
<span class="linenos" data-linenos="35 "></span>        <span class="n">modint</span><span class="o">&lt;</span><span class="n">mod</span><span class="o">&gt;</span> <span class="n">a</span><span class="o">=*</span><span class="k">this</span><span class="p">,</span><span class="n">c</span><span class="o">=</span><span class="mi">1</span><span class="p">;</span>
<span class="linenos" data-linenos="36 "></span>        <span class="k">for</span><span class="p">(;</span><span class="n">b</span><span class="p">;</span><span class="n">b</span><span class="o">&gt;&gt;=</span><span class="mi">1</span><span class="p">,</span><span class="n">a</span><span class="o">*=</span><span class="n">a</span><span class="p">)</span><span class="k">if</span><span class="p">(</span><span class="n">b</span><span class="o">&amp;</span><span class="mi">1</span><span class="p">)</span><span class="n">c</span><span class="o">*=</span><span class="n">a</span><span class="p">;</span>
<span class="linenos" data-linenos="37 "></span>        <span class="k">return</span> <span class="n">x</span><span class="o">=</span><span class="n">c</span><span class="p">.</span><span class="n">x</span><span class="p">,</span><span class="o">*</span><span class="k">this</span><span class="p">;</span>
<span class="linenos" data-linenos="38 "></span>    <span class="p">}</span>
<span class="linenos" data-linenos="39 "></span>    <span class="n">modint</span><span class="o">&lt;</span><span class="n">mod</span><span class="o">&gt;</span> <span class="o">&amp;</span><span class="k">operator</span> <span class="o">/=</span><span class="p">(</span><span class="n">modint</span><span class="o">&lt;</span><span class="n">mod</span><span class="o">&gt;</span> <span class="n">o</span><span class="p">){</span><span class="k">return</span> <span class="o">*</span><span class="k">this</span> <span class="o">*=</span><span class="n">o</span><span class="o">^=</span><span class="n">mod</span><span class="mi">-2</span><span class="p">;}</span>
<span class="linenos" data-linenos="40 "></span>    <span class="n">modint</span><span class="o">&lt;</span><span class="n">mod</span><span class="o">&gt;</span> <span class="o">&amp;</span><span class="k">operator</span> <span class="o">+=</span><span class="p">(</span><span class="kt">int</span> <span class="n">o</span><span class="p">){</span><span class="k">return</span> <span class="n">x</span><span class="o">=</span><span class="n">x</span><span class="o">+</span><span class="n">o</span><span class="o">&gt;=</span><span class="n">mod</span><span class="o">?</span><span class="n">x</span><span class="o">+</span><span class="n">o</span><span class="o">-</span><span class="nl">mod</span><span class="p">:</span><span class="n">x</span><span class="o">+</span><span class="n">o</span><span class="p">,</span><span class="o">*</span><span class="k">this</span><span class="p">;}</span>
<span class="linenos" data-linenos="41 "></span>    <span class="n">modint</span><span class="o">&lt;</span><span class="n">mod</span><span class="o">&gt;</span> <span class="o">&amp;</span><span class="k">operator</span> <span class="o">-=</span><span class="p">(</span><span class="kt">int</span> <span class="n">o</span><span class="p">){</span><span class="k">return</span> <span class="n">x</span><span class="o">=</span><span class="n">x</span><span class="o">-</span><span class="n">o</span><span class="o">&lt;</span><span class="mi">0</span><span class="o">?</span><span class="n">x</span><span class="o">-</span><span class="n">o</span><span class="o">+</span><span class="nl">mod</span><span class="p">:</span><span class="n">x</span><span class="o">-</span><span class="n">o</span><span class="p">,</span><span class="o">*</span><span class="k">this</span><span class="p">;}</span>
<span class="linenos" data-linenos="42 "></span>    <span class="n">modint</span><span class="o">&lt;</span><span class="n">mod</span><span class="o">&gt;</span> <span class="o">&amp;</span><span class="k">operator</span> <span class="o">*=</span><span class="p">(</span><span class="kt">int</span> <span class="n">o</span><span class="p">){</span><span class="k">return</span> <span class="n">x</span><span class="o">=</span><span class="mf">1l</span><span class="n">l</span><span class="o">*</span><span class="n">x</span><span class="o">*</span><span class="n">o</span><span class="o">%</span><span class="n">mod</span><span class="p">,</span><span class="o">*</span><span class="k">this</span><span class="p">;}</span>
<span class="linenos" data-linenos="43 "></span>    <span class="n">modint</span><span class="o">&lt;</span><span class="n">mod</span><span class="o">&gt;</span> <span class="o">&amp;</span><span class="k">operator</span> <span class="o">/=</span><span class="p">(</span><span class="kt">int</span> <span class="n">o</span><span class="p">){</span><span class="k">return</span> <span class="o">*</span><span class="k">this</span> <span class="o">*=</span> <span class="p">((</span><span class="n">modint</span><span class="o">&lt;</span><span class="n">mod</span><span class="o">&gt;</span><span class="p">(</span><span class="n">o</span><span class="p">))</span><span class="o">^=</span><span class="n">mod</span><span class="mi">-2</span><span class="p">);}</span>
<span class="linenos" data-linenos="44 "></span>    <span class="k">template</span><span class="o">&lt;</span><span class="k">class</span> <span class="nc">I</span><span class="o">&gt;</span><span class="k">friend</span> <span class="n">modint</span><span class="o">&lt;</span><span class="n">mod</span><span class="o">&gt;</span> <span class="k">operator</span> <span class="o">+</span><span class="p">(</span><span class="n">modint</span><span class="o">&lt;</span><span class="n">mod</span><span class="o">&gt;</span> <span class="n">a</span><span class="p">,</span><span class="n">I</span> <span class="n">b</span><span class="p">){</span><span class="k">return</span> <span class="n">a</span><span class="o">+=</span><span class="n">b</span><span class="p">;}</span>
<span class="linenos" data-linenos="45 "></span>    <span class="k">template</span><span class="o">&lt;</span><span class="k">class</span> <span class="nc">I</span><span class="o">&gt;</span><span class="k">friend</span> <span class="n">modint</span><span class="o">&lt;</span><span class="n">mod</span><span class="o">&gt;</span> <span class="k">operator</span> <span class="o">-</span><span class="p">(</span><span class="n">modint</span><span class="o">&lt;</span><span class="n">mod</span><span class="o">&gt;</span> <span class="n">a</span><span class="p">,</span><span class="n">I</span> <span class="n">b</span><span class="p">){</span><span class="k">return</span> <span class="n">a</span><span class="o">-=</span><span class="n">b</span><span class="p">;}</span>
<span class="linenos" data-linenos="46 "></span>    <span class="k">template</span><span class="o">&lt;</span><span class="k">class</span> <span class="nc">I</span><span class="o">&gt;</span><span class="k">friend</span> <span class="n">modint</span><span class="o">&lt;</span><span class="n">mod</span><span class="o">&gt;</span> <span class="k">operator</span> <span class="o">*</span><span class="p">(</span><span class="n">modint</span><span class="o">&lt;</span><span class="n">mod</span><span class="o">&gt;</span> <span class="n">a</span><span class="p">,</span><span class="n">I</span> <span class="n">b</span><span class="p">){</span><span class="k">return</span> <span class="n">a</span><span class="o">*=</span><span class="n">b</span><span class="p">;}</span>
<span class="linenos" data-linenos="47 "></span>    <span class="k">template</span><span class="o">&lt;</span><span class="k">class</span> <span class="nc">I</span><span class="o">&gt;</span><span class="k">friend</span> <span class="n">modint</span><span class="o">&lt;</span><span class="n">mod</span><span class="o">&gt;</span> <span class="k">operator</span> <span class="o">/</span><span class="p">(</span><span class="n">modint</span><span class="o">&lt;</span><span class="n">mod</span><span class="o">&gt;</span> <span class="n">a</span><span class="p">,</span><span class="n">I</span> <span class="n">b</span><span class="p">){</span><span class="k">return</span> <span class="n">a</span><span class="o">/=</span><span class="n">b</span><span class="p">;}</span>
<span class="linenos" data-linenos="48 "></span>    <span class="k">friend</span> <span class="n">modint</span><span class="o">&lt;</span><span class="n">mod</span><span class="o">&gt;</span> <span class="k">operator</span> <span class="o">^</span><span class="p">(</span><span class="n">modint</span><span class="o">&lt;</span><span class="n">mod</span><span class="o">&gt;</span> <span class="n">a</span><span class="p">,</span><span class="kt">int</span> <span class="n">b</span><span class="p">){</span><span class="k">return</span> <span class="n">a</span><span class="o">^=</span><span class="n">b</span><span class="p">;}</span>
<span class="linenos" data-linenos="49 "></span>    <span class="k">friend</span> <span class="kt">bool</span> <span class="k">operator</span> <span class="o">==</span><span class="p">(</span><span class="n">modint</span><span class="o">&lt;</span><span class="n">mod</span><span class="o">&gt;</span> <span class="n">a</span><span class="p">,</span><span class="kt">int</span> <span class="n">b</span><span class="p">){</span><span class="k">return</span> <span class="n">a</span><span class="p">.</span><span class="n">x</span><span class="o">==</span><span class="n">b</span><span class="p">;}</span>
<span class="linenos" data-linenos="50 "></span>    <span class="k">friend</span> <span class="kt">bool</span> <span class="k">operator</span> <span class="o">!=</span><span class="p">(</span><span class="n">modint</span><span class="o">&lt;</span><span class="n">mod</span><span class="o">&gt;</span> <span class="n">a</span><span class="p">,</span><span class="kt">int</span> <span class="n">b</span><span class="p">){</span><span class="k">return</span> <span class="n">a</span><span class="p">.</span><span class="n">x</span><span class="o">!=</span><span class="n">b</span><span class="p">;}</span>
<span class="linenos" data-linenos="51 "></span>    <span class="kt">bool</span> <span class="k">operator</span> <span class="o">!</span> <span class="p">()</span> <span class="p">{</span><span class="k">return</span> <span class="o">!</span><span class="n">x</span><span class="p">;}</span>
<span class="linenos" data-linenos="52 "></span>    <span class="n">modint</span><span class="o">&lt;</span><span class="n">mod</span><span class="o">&gt;</span> <span class="k">operator</span> <span class="o">-</span> <span class="p">()</span> <span class="p">{</span><span class="k">return</span> <span class="n">x</span><span class="o">?</span><span class="n">mod</span><span class="o">-</span><span class="nl">x</span><span class="p">:</span><span class="mi">0</span><span class="p">;}</span>
<span class="linenos" data-linenos="53 "></span>    <span class="n">modint</span><span class="o">&lt;</span><span class="n">mod</span><span class="o">&gt;</span> <span class="o">&amp;</span><span class="k">operator</span><span class="o">++</span><span class="p">(</span><span class="kt">int</span><span class="p">){</span><span class="k">return</span> <span class="o">*</span><span class="k">this</span><span class="o">+=</span><span class="mi">1</span><span class="p">;}</span>
<span class="linenos" data-linenos="54 "></span><span class="p">};</span>
<span class="linenos" data-linenos="55 "></span><span class="k">typedef</span> <span class="n">modint</span><span class="o">&lt;</span><span class="n">mod</span><span class="o">&gt;</span><span class="n">mint</span><span class="p">;</span>
<span class="linenos" data-linenos="56 "></span><span class="n">mint</span> <span class="n">t</span><span class="p">[]</span><span class="o">=</span><span class="p">{</span><span class="mi">0</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span><span class="mi">24</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">240</span><span class="p">,</span><span class="mi">204</span><span class="p">,</span><span class="mi">1316</span><span class="p">,</span><span class="mi">2988</span><span class="p">,</span><span class="mi">6720</span><span class="p">,</span> 
<span class="linenos" data-linenos="57 "></span> <span class="mi">26200</span><span class="p">,</span><span class="mi">50248</span><span class="p">,</span><span class="mi">174280</span><span class="p">,</span><span class="mi">436904</span><span class="p">,</span><span class="mi">1140888</span><span class="p">,</span> 
<span class="linenos" data-linenos="58 "></span> <span class="mi">3436404</span><span class="p">,</span><span class="mi">8348748</span><span class="p">,</span><span class="mi">24631232</span><span class="p">,</span><span class="mi">64575924</span><span class="p">,</span> 
<span class="linenos" data-linenos="59 "></span> <span class="mi">174658944</span><span class="p">,</span><span class="mi">488230244</span><span class="p">};</span><span class="c1">//初始转移 </span>
<span class="linenos" data-linenos="60 "></span><span class="n">mint</span> <span class="n">X</span><span class="p">[</span><span class="mi">17</span><span class="p">]</span><span class="o">=</span><span class="p">{</span>
<span class="linenos" data-linenos="61 "></span><span class="mi">0</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">8</span><span class="p">,</span><span class="mi">-1</span><span class="p">,</span><span class="mi">16</span><span class="p">,</span><span class="mi">-10</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">-12</span><span class="p">,</span><span class="mi">-48</span><span class="p">,</span> 
<span class="linenos" data-linenos="62 "></span><span class="mi">26</span><span class="p">,</span><span class="mi">-44</span><span class="p">,</span><span class="mi">15</span><span class="p">,</span><span class="mi">-16</span><span class="p">,</span><span class="mi">-4</span><span class="p">,</span><span class="mi">-4</span><span class="p">,</span><span class="mi">-1</span>
<span class="linenos" data-linenos="63 "></span><span class="p">};</span>
<span class="linenos" data-linenos="64 "></span><span class="kt">signed</span> <span class="nf">main</span><span class="p">(){</span>
<span class="linenos" data-linenos="65 "></span>    <span class="kt">int</span> <span class="n">T</span><span class="p">;</span><span class="n">in</span><span class="o">::</span><span class="n">read</span><span class="p">(</span><span class="n">T</span><span class="p">);</span>
<span class="linenos" data-linenos="66 "></span>    <span class="k">while</span><span class="p">(</span><span class="n">T</span><span class="o">--</span><span class="p">){</span>
<span class="linenos" data-linenos="67 "></span>        <span class="kt">long</span> <span class="kt">long</span> <span class="n">n</span><span class="o">=</span><span class="mi">100000</span><span class="p">;</span>
<span class="linenos" data-linenos="68 "></span>        <span class="n">in</span><span class="o">::</span><span class="n">read</span><span class="p">(</span><span class="n">n</span><span class="p">);</span>
<span class="linenos" data-linenos="69 "></span>        <span class="c1">//求 x^n % (1-C)</span>
<span class="linenos" data-linenos="70 "></span>        <span class="n">vector</span><span class="o">&lt;</span><span class="n">mint</span><span class="o">&gt;</span><span class="n">res</span><span class="p">,</span><span class="n">a</span><span class="p">;</span>
<span class="linenos" data-linenos="71 "></span>        <span class="n">res</span><span class="p">.</span><span class="n">resize</span><span class="p">(</span><span class="mi">17</span><span class="p">);</span><span class="n">res</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">=</span><span class="mi">1</span><span class="p">;</span>
<span class="linenos" data-linenos="72 "></span>        <span class="n">a</span><span class="p">.</span><span class="n">resize</span><span class="p">(</span><span class="mi">17</span><span class="p">);</span><span class="n">a</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">=</span><span class="mi">1</span><span class="p">;</span>
<span class="linenos" data-linenos="73 "></span>        <span class="k">auto</span> <span class="n">mul</span><span class="o">=</span><span class="p">[</span><span class="o">&amp;</span><span class="p">](</span><span class="n">vector</span><span class="o">&lt;</span><span class="n">mint</span><span class="o">&gt;</span><span class="n">A</span><span class="p">,</span><span class="n">vector</span><span class="o">&lt;</span><span class="n">mint</span><span class="o">&gt;</span><span class="n">B</span><span class="p">){</span>
<span class="linenos" data-linenos="74 "></span>            <span class="c1">//相乘并取模 </span>
<span class="linenos" data-linenos="75 "></span>            <span class="n">vector</span><span class="o">&lt;</span><span class="n">mint</span><span class="o">&gt;</span> <span class="n">C</span><span class="p">;</span><span class="n">C</span><span class="p">.</span><span class="n">resize</span><span class="p">(</span><span class="mi">40</span><span class="p">);</span>
<span class="linenos" data-linenos="76 "></span>            <span class="k">for</span><span class="p">(</span><span class="kt">int</span> <span class="n">i</span><span class="o">=</span><span class="mi">0</span><span class="p">;</span><span class="n">i</span><span class="o">&lt;</span><span class="n">A</span><span class="p">.</span><span class="n">size</span><span class="p">();</span><span class="n">i</span><span class="o">++</span><span class="p">)</span>
<span class="linenos" data-linenos="77 "></span>                <span class="k">for</span><span class="p">(</span><span class="kt">int</span> <span class="n">j</span><span class="o">=</span><span class="mi">0</span><span class="p">;</span><span class="n">j</span><span class="o">&lt;</span><span class="n">B</span><span class="p">.</span><span class="n">size</span><span class="p">();</span><span class="n">j</span><span class="o">++</span><span class="p">)</span>
<span class="linenos" data-linenos="78 "></span>                    <span class="n">C</span><span class="p">[</span><span class="n">i</span><span class="o">+</span><span class="n">j</span><span class="p">]</span><span class="o">+=</span><span class="n">A</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">*</span><span class="n">B</span><span class="p">[</span><span class="n">j</span><span class="p">];</span>
<span class="linenos" data-linenos="79 "></span>            <span class="k">for</span><span class="p">(</span><span class="kt">int</span> <span class="n">i</span><span class="o">=</span><span class="n">C</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="mi">-1</span><span class="p">;</span><span class="n">i</span><span class="o">&gt;=</span><span class="mi">16</span><span class="p">;</span><span class="n">i</span><span class="o">--</span><span class="p">){</span>
<span class="linenos" data-linenos="80 "></span>                <span class="k">if</span><span class="p">(</span><span class="n">C</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">!=</span><span class="mi">0</span><span class="p">){</span>
<span class="linenos" data-linenos="81 "></span>                    <span class="k">for</span><span class="p">(</span><span class="kt">int</span> <span class="n">k</span><span class="o">=</span><span class="mi">0</span><span class="p">;</span><span class="n">k</span><span class="o">&lt;=</span><span class="mi">16</span><span class="p">;</span><span class="n">k</span><span class="o">++</span><span class="p">)</span>
<span class="linenos" data-linenos="82 "></span>                        <span class="n">C</span><span class="p">[</span><span class="n">i</span><span class="o">-</span><span class="n">k</span><span class="p">]</span><span class="o">+=</span><span class="n">C</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">*</span><span class="n">X</span><span class="p">[</span><span class="n">k</span><span class="p">];</span>
<span class="linenos" data-linenos="83 "></span>                    <span class="n">C</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">=</span><span class="mi">0</span><span class="p">;</span>
<span class="linenos" data-linenos="84 "></span>                <span class="p">}</span>
<span class="linenos" data-linenos="85 "></span>            <span class="p">}</span> 
<span class="linenos" data-linenos="86 "></span>            <span class="n">C</span><span class="p">.</span><span class="n">resize</span><span class="p">(</span><span class="mi">17</span><span class="p">);</span>
<span class="linenos" data-linenos="87 "></span>            <span class="k">return</span> <span class="n">C</span><span class="p">;</span>
<span class="linenos" data-linenos="88 "></span>        <span class="p">}</span> <span class="p">;</span>
<span class="linenos" data-linenos="89 "></span>        <span class="k">while</span><span class="p">(</span><span class="n">n</span><span class="p">){</span>
<span class="linenos" data-linenos="90 "></span>            <span class="k">if</span><span class="p">(</span><span class="n">n</span><span class="o">&amp;</span><span class="mi">1</span><span class="p">)</span><span class="n">res</span><span class="o">=</span><span class="n">mul</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="n">a</span><span class="p">);</span>
<span class="linenos" data-linenos="91 "></span>            <span class="n">a</span><span class="o">=</span><span class="n">mul</span><span class="p">(</span><span class="n">a</span><span class="p">,</span><span class="n">a</span><span class="p">);</span><span class="n">n</span><span class="o">&gt;&gt;=</span><span class="mi">1</span><span class="p">;</span>
<span class="linenos" data-linenos="92 "></span>        <span class="p">}</span>
<span class="linenos" data-linenos="93 "></span>        <span class="n">mint</span> <span class="n">ans</span><span class="o">=</span><span class="mi">0</span><span class="p">;</span>
<span class="linenos" data-linenos="94 "></span>        <span class="k">for</span><span class="p">(</span><span class="kt">int</span> <span class="n">i</span><span class="o">=</span><span class="mi">0</span><span class="p">;</span><span class="n">i</span><span class="o">&lt;=</span><span class="mi">16</span><span class="p">;</span><span class="n">i</span><span class="o">++</span><span class="p">)</span>
<span class="linenos" data-linenos="95 "></span>            <span class="n">ans</span><span class="o">+=</span><span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">*</span><span class="n">t</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
<span class="linenos" data-linenos="96 "></span>        <span class="n">out</span><span class="o">::</span><span class="n">write</span><span class="p">(</span><span class="n">ans</span><span class="p">.</span><span class="n">x</span><span class="p">);</span><span class="n">out</span><span class="o">::</span><span class="n">putc</span><span class="p">(</span><span class="sc">&#39;\n&#39;</span><span class="p">);</span>
<span class="linenos" data-linenos="97 "></span>    <span class="p">}</span>
<span class="linenos" data-linenos="98 "></span>    <span class="n">out</span><span class="o">::</span><span class="n">flush</span><span class="p">();</span>
<span class="linenos" data-linenos="99 "></span><span class="p">}</span>
</code></pre></div>
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